June 6, 2009
MJD
Moving Straight Ahead 5.2
How steep is that line? Many real world situations can be modeled and predicted using mathematics.
Do parts A-D for each equation below.
i. y=2x
ii. y=-3x
iii. y=5+2x
iv. y=1/2x+2
v. y=2-3x
A. Make a table of the x and y values for the equation. Use the x values -3, -2, -1, 0, 1, 2, 3, and 4.
B. On grid paper make a graph of the equation. i: red, ii: green, iii: blue, iv: yellow
PART 2 of the graph
v: red
c. choose two points on the line, and compute the ratio of vertical change to the horizontal change from one point to the other. Would you get the same ratio if you had chosen two different points? Choose two different points, and check your answer.
i. 0, 0 and 2, 2 ratio: +1 horizontal for +2 vertical
ii. 0,0 and -1, 3 ratio: +1 horizontal for -3 vertical
iii. -5, -5 and 0, 5 ratio: +1 horizontal for +2 vertical
iv. -2, 1 and 0, 2 ratio: +1 horizontal for + 0.5 vertical
v. -1, 5 and 4, -10 ratio: +1 horizontal for -3 vertical.
Yes you would get the same ratio as the line is constant and will stay in that increase or decrease forever.
d. The ratio you computed in part c is the slope of a line, How is the slope of the line related to the table of values for the line? how is it related to the equation for the line?
It is related to the values for the line as values cause slopes, and the difference between the value and the axis its on for example x to y, causes it also. Two uneven x and y's make a steeper graph. It is related to the equation of the line, because the equation makes the table's information, which makes the graphs information, so the slope changes as the equation does, and again if x and y are very far from even then they make a steep graph.
Follow-Up
Use the ideas you have learned about slope and about vertical and horizontal change to explain why the line of y=3x is steeper than the line for y=x.
The line for y=3x is steeper because this means that the y line goes up 3 values per x value, and in y=x, the y value goes up one value per x value. So three to 1 is around a 70 degree angle up, where y=x is 1 to 1 making a 45 degree angle going up, if it is an even measurement between each value.
MJD
Moving Straight Ahead 5.2
How steep is that line?
Many real world situations can be modeled and predicted using mathematics.
Do parts A-D for each equation below.
i. y=2x
ii. y=-3x
iii. y=5+2x
iv. y=1/2x+2
v. y=2-3x
A. Make a table of the x and y values for the equation. Use the x values -3, -2, -1, 0, 1, 2, 3, and 4.
B. On grid paper make a graph of the equation. i: red, ii: green, iii: blue, iv: yellow
PART 2 of the graph
v: red
c. choose two points on the line, and compute the ratio of vertical change to the horizontal change from one point to the other. Would you get the same ratio if you had chosen two different points? Choose two different points, and check your answer.
i. 0, 0 and 2, 2 ratio: +1 horizontal for +2 vertical
ii. 0,0 and -1, 3 ratio: +1 horizontal for -3 vertical
iii. -5, -5 and 0, 5 ratio: +1 horizontal for +2 vertical
iv. -2, 1 and 0, 2 ratio: +1 horizontal for + 0.5 vertical
v. -1, 5 and 4, -10 ratio: +1 horizontal for -3 vertical.
Yes you would get the same ratio as the line is constant and will stay in that increase or decrease forever.
d. The ratio you computed in part c is the slope of a line, How is the slope of the line related to the table of values for the line? how is it related to the equation for the line?
It is related to the values for the line as values cause slopes, and the difference between the value and the axis its on for example x to y, causes it also. Two uneven x and y's make a steeper graph. It is related to the equation of the line, because the equation makes the table's information, which makes the graphs information, so the slope changes as the equation does, and again if x and y are very far from even then they make a steep graph.
Follow-Up
Use the ideas you have learned about slope and about vertical and horizontal change to explain why the line of y=3x is steeper than the line for y=x.
The line for y=3x is steeper because this means that the y line goes up 3 values per x value, and in y=x, the y value goes up one value per x value. So three to 1 is around a 70 degree angle up, where y=x is 1 to 1 making a 45 degree angle going up, if it is an even measurement between each value.